The angles between the two altitudes through d vertex of obtuse angles of a parallelogram is 50 find d - Maths -

Question

The angles between the two altitudes through d vertex of
obtuse angles of a parallelogram is 50 find d obtuse angle

Priyanka Kedia · Accepted Answer

Let ABCD be a parallelogram DM and DN is perpendicular to side AB and BC respectively $G i v e n, ∠ M D N = 50^{0}$ From figure, MDNB is a quadrilateral So, $∠ M D N + ∠ D N B + ∠ N B M + ∠ B M D = 360^{0} \Rightarrow 50^{0} + 90^{0} + ∠ N B M + 90^{0} = 360^{0} \Rightarrow ∠ N B M = 130^{0} \Rightarrow ∠ B = 130^{0}$ In a parallelogram opposites angles are congruent and adjacent angles are supplementary $∠ B = ∠ D = 130^{0} A n d, ∠ B + ∠ C = 180^{0} \Rightarrow 130^{0} + ∠ C = 180^{0} \Rightarrow ∠ C = 50^{0} T h u s, ∠ A = ∠ C = 50^{0}$ Hence, the obtuse angle is $130^{0}$

The angles between the two altitudes through d vertex of obtuse angles of a parallelogram is 50..find d obtuse angle..